Beezy :
i know minecraft only uses one core, but idk about LoL. Generally extra cores help with the stream, because main cores run the game and the 'side' core handle the stream. you are only dealing with 2 cores total, and not too strong of cores really.
the next issue is the GPU, its on the weaker side. meant more for high definition video than gaming really. Gaming will be a struggle enough with that GPU, streaming it wont do the performance any justice.
really you can only know by trying. look into some free software before you invest money
I hope this isn't to off topic but. I'm not sure if that minecraft only using 1 core thing is true. I know it was in the past but with the change to the way singleplayer and servers essentially got merged, along with the changes that made things much more threaded, such as chunk loading and mods like optifine it would be rather odd for it to be only single core still.
Don't get me wrong, not saying you are wrong. Just saying it would extremely stupid for it to still in this day and age to be single core locked.